French President Francois Hollande sent his "condolences to the families of the victims" as shocked residents grouped around the scene of the accident on a council estate in the Champagne region.
"The toll is near-definitive," said the top official of the Marne region, Pierre Dartout, following reports that a young man was being sought. "All the tenants have been accounted for."
Local authorities said the "probable" cause of the accident - which saw the extremity of a four-storey building containing some 10 flats crash down - was a gas explosion.
Police said three adults were killed and another 14 people injured, one seriously. Among the hurt were children, they added.
A 60-year-old woman was found dead in the rubble several hours after the collapse, bringing the death toll up to three.
Some 75 residents gathered in a nearby sports complex and a school where counsellors were available for the traumatised.
At the beginning of the month, four people from the same family were killed and another person seriously injured when a gas explosion devastated their council flat in Witry-les-Reims, not far from the scene of Sunday's accident.
That incident shocked the neighbourhood, particularly as the father had still been alive when firefighters arrived, talking to them for over two hours to try to help them locate his wife and child, before dying in the ambulance.
On Sunday, one council estate resident whose section of the building had not been affected said he heard a huge explosion that shook the walls and broke windows.
"When I looked through the window, I saw that the building had collapsed like a pack of cards, with lots of smoke. I heard people screaming," said the resident, who would only be cited as Rafik.
The building - built in the 1960s and one of the oldest in the area - had been renovated several years ago.
"They only re-painted the facade, the interior has not changed since the 1960s. This was bound to happen, it's too old here," said one by-stander named Abdelkader.
"Judging by the state of the buildings, this doesn't surprise me. Here when you put a nail in the wall, it crumbles," said another nearby resident called Raissa.
In a statement, Hollande deplored a "terrible tragedy" and expressed his "solidarity to the city of Reims."
Housing Minister Cecile Duflot told French radio that an "extensive investigation" would take place, adding that a gas explosion was "the most likely hypothesis" for the disaster
"It seems that the building was well maintained, the correct checks had been carried out on the appliances," she added.